Early Warning Signals for Critical Transitions?

The effec­tive man­age­ment of nat­ural resource pop­u­la­tions such as fish­eries or forests and the ecosys­tems in which they are embed­ded is a cen­tral goal of much work in both the­o­ret­i­cal and applied eco­log­i­cal research. Man­age­ment deci­sions must be made in an uncer­tain world, cop­ing with errors in data, uncer­tainty in model para­me­ters and even the choice of mod­els used. Advances in areas such as risk man­age­ment, opti­miza­tion under uncer­tainty and adap­tive man­age­ment meth­ods have offered a way for­ward in spite of such uncer­tainty. We have only to admit what we don’t know, and make the best deci­sion based on the infor­ma­tion at hand.

The real­iza­tion that such com­plex sys­tems can con­tain tip­ping points — thresh­olds at which the sys­tem can tran­si­tion into a less desir­able state rapidly and with lit­tle warn­ing — poses a fun­da­men­tal chal­lenge to these approaches. Such approaches require that we know what we don’t know: We don’t use the best guess of a para­me­ter; instead, we have a dis­tri­b­u­tion of pos­si­ble val­ues it may take. As recent events in the econ­omy have illus­trated, esti­mat­ing the dis­tri­b­u­tion isn’t easy, and for com­plex sys­tems with alternate sta­ble states, a lit­tle bit more uncer­tainty can make a big dif­fer­ence. How then do we make the best deci­sion based on the infor­ma­tion avail­able without expos­ing the sys­tem to these sud­den crashes? How do we han­dle that uncertainty we just can­not para­me­ter­ize — the unknown unknowns?

We com­bine meth­ods from opti­mal con­trol and stochastic dynamic pro­gram­ming with meth­ods from eco­log­i­cal resilience and early warning sig­nals to study both simulated­­ and empir­i­cal exam­ples of these systems.